Question

A 20m deep well with diameter 7m is dug, and the earth from digging is evenly spread out to form a platform 22m by 14m. Find the height of the platform.

Answer 1

Hint: Use the fact that the amount of soil extracted from the well will remain the same and will form the platform. Use the fact that the volume of a cylinder of radius r and height h is given by $\pi {{r}^{2}}h$ , and the volume of a cuboid of length l, breadth b and height h is given by lbh. Assume that the height of the platform be h. Hence find the volume of the platform in terms of h. Equate this volume to the volume of the well and hence form a linear equation in h. Solve the equation to get the value of h. The value of h will be the height of the platform.

Complete step-by-step answer:

Finding the volume of the well:
We have the diameter of the well = 7m.
Hence the radius of the well = 3.5m.
Depth of the well = h = 20m.
Hence the volume of the earth removed by digging $=\pi {{r}^{2}}h=\dfrac{22}{7}\times {{\left( 3.5 \right)}^{2}}\times 20=770$ cubic metres.
Let the height of the platform be h.

Here length of the platform = l = 22m
Breadth of the platform = b = 14m
Height of the platform = h
We know that the volume of a cuboid of length l, breadth b and height h is given by lbh.
Hence the volume of the platform $=22\times 14\times h=308h$
Since the platform is made of earth obtained from digging, we have
The volume of platform = Volume of earth
Hence we have $308h=770$
Dividing both sides by 308, we get
$h=\dfrac{770}{308}=2.5$ metres.
Hence the height of the platform = 2.5m

Note: Verification:
The volume of cuboid = $22\times 14\times 2.5=770$
The volume of the well $=\pi {{r}^{2}}h=770$
Hence, the volume of the well = the volume of the cuboid. Hence our answer is correct.